Abstract

Abstract. We explicitly address the fundamental issue of member diversity in multi-model ensembles. To date, no attempts in this direction have been documented within the air quality (AQ) community despite the extensive use of ensembles in this field. Common biases and redundancy are the two issues directly deriving from lack of independence, undermining the significance of a multi-model ensemble, and are the subject of this study. Shared, dependant biases among models do not cancel out but will instead determine a biased ensemble. Redundancy derives from having too large a portion of common variance among the members of the ensemble, producing overconfidence in the predictions and underestimation of the uncertainty. The two issues of common biases and redundancy are analysed in detail using the AQMEII ensemble of AQ model results for four air pollutants in two European regions. We show that models share large portions of bias and variance, extending well beyond those induced by common inputs. We make use of several techniques to further show that subsets of models can explain the same amount of variance as the full ensemble with the advantage of being poorly correlated. Selecting the members for generating skilful, non-redundant ensembles from such subsets proved, however, non-trivial. We propose and discuss various methods of member selection and rate the ensemble performance they produce. In most cases, the full ensemble is outscored by the reduced ones. We conclude that, although independence of outputs may not always guarantee enhancement of scores (but this depends upon the skill being investigated), we discourage selecting the members of the ensemble simply on the basis of scores; that is, independence and skills need to be considered disjointly.

Highlights

  • M ensemble of among other techquality (AQ) model results for four air pollutants in two bles relies on the fundamental assumption that information

  • – Independence, a formal property, when the joint probability distribution function (PDF) of two or more models is derived from the product of single PDFs (Cover and Thomas, 2006)

  • We investigate the correlation between errors produced by AQ models run by 12 groups in the context of the Air Quality Modelling Evaluation International Initiative (AQMEII) (Rao et al, 2011)

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Summary

Introduction

M ensemble of AQ model results for four air pollutants in two bles relies on the fundamental assumption that information. – Independence, a formal property, when the joint probability distribution function (PDF) of two or more models is derived from the product of single PDFs (Cover and Thomas, 2006). This is the rigorous definition of independence, though the joint PDF is difficult to estimate in practice. Models are said to be diverse when they are developed starting from different conceptual basis and are based on different causal assumptions. Their outputs (and errors) can be correlated. Outputs and errors of similar models are expected to be highly correlated

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